Abstract
This paper proves the decidability of entailments in separation logic with monadic inductive definitions and implicit existentials. This system is obtained from the bounded-treewidth separation logic SLRDbtw of Iosif et al. in 2013 by adding implicit existential variables and restricting inductive definitions to monadic ones. The system proposed in this paper is a decidable system where one can use general recursive data structures with pointers as data, such as lists of pointers. The key idea is to reduce the problem to the decidability of SLRDbtw, by assigning local addresses or some distingu ished address to implicit existential variables so that the resulting definition clauses satisfy the establishment condition of SLRDbtw. This paper also proves the undecidability of the entailments when one adds implicit existentials to SLRDbtw. This shows that the implicit existentials are critical for the decidability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Antonopoulos, T., Gorogiannis, N., Haase, C., Kanovich, M., Ouaknine, J.: Foundations for decision problems in separation logic with general inductive predicates. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 411–425. Springer, Heidelberg (2014)
Berdine, J., Calcagno, C., O’Hearn, P.W.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004)
Berdine, J., Calcagno, C., O’Hearn, P.W.: Symbolic execution with separation logic. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005)
Brotherston, J., Distefano, D., Petersen, R.L.: Automated cyclic entailment proofs in separation logic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 131–146. Springer, Heidelberg (2011)
Brotherston, J., Gorogiannis, N., Petersen, R.L.: A generic cyclic theorem prover. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 350–367. Springer, Heidelberg (2012)
Cook, B., Haase, C., Ouaknine, J., Parkinson, M., Worrell, J.: Tractable reasoning in a fragment of separation logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 235–249. Springer, Heidelberg (2011)
Enea, C., Saveluc, V., Sighireanu, M.: Compositional invariant checking for overlaid and nested linked lists. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 129–148. Springer, Heidelberg (2013)
Enea, C., Lengál, O., Sighireanu, M., Vojnar, T.: Compositional entailment checking for a fragment of separation logic. In: Garrigue, J. (ed.) APLAS 2014. LNCS, vol. 8858, pp. 314–333. Springer, Heidelberg (2014)
Iosif, R., Rogalewicz, A., Simacek, J.: The tree width of separation logic with recursive definitions. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 21–38. Springer, Heidelberg (2013)
Iosif, R., Rogalewicz, A., Vojnar, T.: Deciding entailments in inductive separation logic with tree automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 201–218. Springer, Heidelberg (2014)
Nguyen, H.H., Chin, W.-N.: Enhancing program verification with lemmas. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 355–369. Springer, Heidelberg (2008)
Piskac, R., Wies, T., Zufferey, D.: Automating separation logic using SMT. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 773–789. Springer, Heidelberg (2013)
Piskac, R., Wies, T., Zufferey, D.: Automating separation logic with trees and data. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 711–728. Springer, Heidelberg (2014)
Navarro Pérez, J.A., Rybalchenko, A.: Separation logic modulo theories. In: Shan, C. (ed.) APLAS 2013. LNCS, vol. 8301, pp. 90–106. Springer, Heidelberg (2013)
Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: Proceedings of Seventeenth Annual IEEE Symposium on Logic in Computer Science (LICS2002), pp. 55–74 (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Tatsuta, M., Kimura, D. (2015). Separation Logic with Monadic Inductive Definitions and Implicit Existentials. In: Feng, X., Park, S. (eds) Programming Languages and Systems. APLAS 2015. Lecture Notes in Computer Science(), vol 9458. Springer, Cham. https://doi.org/10.1007/978-3-319-26529-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-26529-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26528-5
Online ISBN: 978-3-319-26529-2
eBook Packages: Computer ScienceComputer Science (R0)